New Synchronous Computation Dynamics for Hopfield Networks

The dynamics of the original Hopfield network is asynchronous (sequential) (updates the state of only one neuron per time step). In this paper, we propose a new tool and a new dynamics to reduce the processing time by updating one or more neurons simultaneously per instant while ensuring process convergence and aiming for the maximum energy decrease at each step, thus guaranteeing the shortest total processing time. From the point of view of synchronous dynamics, calculating the next network state at which energy decreases the most from the current state while ensuring convergence is itself a combinatorial optimization problem. We develop and use a new tool to solve it. We call this new tool Discrete Differential Filter (DDF) and, based upon it, we develop a new synchronous dynamics which we call SD-DDF (Synchronous Dynamics based upon Discrete Differential Filter). In this paper, we review the original asynchronous dynamics for Hopfield networks and present a new tool and a new synchronous dynamics with its theoretical justification and four computational experiments to assess the speed up in processing time empirically.